Vibrational properties of the Au-($\sqrt{3}\times \sqrt{3}$)/Si(111) surface reconstruction

The vibrational properties of the Au-induced ($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ reconstruction of the Si(111) surface are investigated by polarized surface Raman spectroscopy and density-functional theory. The Raman measurements are performed in situ at room temperature as well as 20 K, and they reveal the presence of vibrational eigenmodes in the spectral range from 20 to 450 ${\mathrm{cm}}^{-1}$. In particular, two peaks of $E$ symmetry at 75 and 183 ${\mathrm{cm}}^{-1}$ dominate the spectra. No substantial difference between room- and low-temperature spectra is observed, suggesting that the system does not undergo a phase transition down to 20 K. First-principles calculations are performed based on the structural models discussed in the literature. The thermodynamically stable conjugate honeycomb-chained-trimer model (CHCT) [Surf. Sci. 275, L691 (1992)] leads to phonon eigenvalues compatible with the experimental observations in the investigated spectral range. On the basis of the phonon eigenfrequencies, symmetries, and Raman intensities, we assign the measured spectral features to the calculated phonon modes. The good agreement between measured and calculated modes provides a strong argument in favor of the CHCT model.

Figure 1

Structural models of the Au-($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ reconstruction on Si(111). (a) Twisted-trimer (TT) model, (b) conjugate honeycomb-chained-trimer (CHCT) model, (c) honeycomb-chained-trimer (HCT) model, and (d) ${\mathrm{H}}_3$-missing-top-layer (${\mathrm{H}}_3$-MTL) model. Au atoms in yellow, Si atoms in blue, and topmost Si atoms in light blue. The substrate ($1\times 1$) and the ($\sqrt{3}\times \sqrt{3}$) reconstructed surface unit cells as well as mirror symmetry planes are indicated. See text for further details.

Figure 2

LEED pattern of Au-($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$/Si(111) at room temperature. Electron energy $E=80$ eV. The blue and green rhomb denote the ($1\times 1$)- and the Au-($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ unit cell, respectively.

Figure 3

Waterfall plot of the Raman spectra of Au-($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$/Si(111) for the polarization configuration $z\left(xx\right)\overline{z}$ + $z\left(xy\right)\overline{z}$ for room temperature (RT, red) and $T\approx 20$ K (LT, blue). For both cases, as a reference the aged and unreconstructed Si(111) is plotted (black). The additional intensity features of the Au-covered surfaces are attributed to the Au-($\sqrt{3}\times \sqrt{3}$) reconstruction. The highlighted spectral range up to 200 ${\mathrm{cm}}^{-1}$ is analyzed in more detail and plotted on an extended frequency scale in the following figures. The green arrows indicate Au-induced features at higher frequencies.

Figure 4

Raman intensity difference between the Au-($\sqrt{3}\times \sqrt{3})R{30}^{\circ }$/Si(111) and the unreconstructed Si(111) reference surface for the polarization configuration $z\left(xx\right)\overline{z}$ + $z\left(xy\right)\overline{z}$: (a) room temperature (RT), (b) low temperature (LT, $T\approx 20$ K). The phonon peaks shift slightly to higher wave numbers after cooling. Note the arising peak at 183 ${\mathrm{cm}}^{-1}$ (green arrow) at LT.

Figure 5

Polarization-dependent difference spectra of Au-($\sqrt{3}\times \sqrt{3}$)/Si(111) for low temperature (LT, $T\approx 20$ K): (a) polarization configuration $z\left(xx\right)\overline{z}$, (b) polarization configuration $z\left(xy\right)\overline{z}$. The spectra are fitted with Voigt profiles (full lines) and plotted together with the cumulative fit (black).

Figure 6

Raman spectrum of the Au-($\sqrt{3}\times \sqrt{3}$)/Si(111) surface reconstruction calculated for the ($xx$) polarization according to the (a) CHCT model and the (b) TT model within the DFT-GGA. Dashed lines show experimentally observed features that have vanishing intensity in our calculations. They do not contribute to the cumulative spectrum (black).

Figure 7

Displacement pattern of selected phonon modes in the CHCT structure calculated within DFT-GGA at (a) 17, (b) 45, (c) 128, and (d) 205 ${\mathrm{cm}}^{-1}$. The arrows show the atomic displacement within the ($\sqrt{3}\times \sqrt{3}$) surface unit cell. The symmetry-preserving modes [(b) and (c)] are $A$-type, the symmetry-reducing ones [(a) and (d)] are $E$-type.